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Lyapunov Stability of a Class of Operator Integro-differential Equations with Applications to Viscoelasticity

✍ Scribed by A. Drozdov

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 785 KB
Volume: 19
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(19960325)19:5<341::aid-mma775>3.0.co;2-m

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✦ Synopsis

Communicated by G. F. Roach

The Lyapunov stability is analysed for a class of integro-differential equations with unbounded operator coefficients. These equations arise in the study of non-conservative stability problems for viscoelastic thin-walled elements of structures. Some sufficient stability conditions are derived by using the direct Lyapunov method. These conditions are formulated for arbitrary kernels of the Volterra integral operator in terms of norms of the operator coefficients. Employing these conditions the supersonic flutter of a viscoelastic panel is studied and explicit expressions for the critical gas velocity are derived. Dependence of the critical flow velocity on the material characteristics and compressive load is analysed numerically.

Furthermore, there exist positive constants T1 and T 2 , T1 < T 2 , such that for any t > O CCC 017C&4214/96/0S0341-21

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